The probability of two events happening at the same time

3 earthquakes happened on day 15, 16, and 17. During these days, a temperature increase was observed apparently because of the earthquakes.
But temperature also increases on other days. So, we don't know for sure if the temperature increase was triggered by the earthquakes or not, -maybe it was just weather. But we can calculate some confidence level or probability that the temperature increased because of the earthquake by using the information from the graph. Does anyone have any tips on how to do so?

From the graph it does look like there is a strong correlation. If you want to put a number on it, simply take the temperature points (controlling for seasons) and compute the mean/std. Next find the probability of finding those points from a gaussian. This will tell the likelihood of observing those higher temperatures.